Prove that a- b- -a- b- - a- 2 - b- 2 if and only if a-b- are perpendicular- given a-0- b-0-

To prove : (a⃗ + b⃗)(a⃗+ b⃗)= |a⃗|^2+ |b⃗|^2 #160;Given, a⃗ and b⃗ are perpendicular #160;Proof since a⃗ and b⃗ are perpendicu ...

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Applications of Dot Product

Prove that ...

Question

Prove that $(\to a + \to b) \cdot (\to a + \to b) = {| \to a |}^{2} + {∣ ∣ \to b ∣ ∣}^{2}$ if and only if $\to a \to b$ are perpendicular, given $\to a \neq \to 0, \to b \neq \to 0$

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$\to a \neq \to 0, \to b \neq \to 0, \to a \times \to b = \to 0, \to c \times \to b = \to 0 \Rightarrow \to a \times \to c =$

| \to a | = 2, ∣ ∣ \to b ∣ ∣ = 3

\to a, \to b

\to 0, \to a + \to b, \to a - \to b

\to a + \to b + \to c = \to 0

\to a \times \to b = \to b \times \to c = \to c \times \to a

\to a, \to b, \to c

\to a + \to b + \to c = \to 0

(\to a, \to b) = \frac{π}{3}

| \to a \times \to b | + | \to b \times \to c | + | \to c \times \to a | =

\to a, \to b, \to c

\to a + \to b + \to c = \to 0

(\to a, \to b) = \frac{π}{3}

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

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